CHI-SQUARE TEST

A 'chi-square test' is any statistical hypothesis test in which the test statistic has a chi-square distribution when the null hypothesis is true, or any in which the probability distribution of the test statistic (assuming the null hypothesis is true) can be made to approximate a chi-square distribution as closely as desired by making the sample size large enough.
Specifically, a chi-square test for independence evaluates statistically significant differences between proportions for two or more groups in a data set.

★ Pearson's chi-square test, also known as the Chi-square goodness-of-fit test, commonly referred to as ''the'' chi-square test

★ Yates' chi-square test also known as Yates' correction for continuity

★ Mantel-Haenszel chi-square test

★ Linear-by-linear association chi-square test

Contents

Significance and effect size

See also

External links

References

Significance and effect size

In the social sciences, the significance of the chi-square statistic is often given in terms of a p value (e.g., ''p'' = 0.05). It is an indication of the likelihood of obtaining a result (0.05 = 5%). As such, it is relatively uninformative. A more helpful accompanying statistic is phi (or Cramer's phi, or Cramer's V).^[1] Phi is a measure of association that reports a value for the correlation between the two dichotomous variables compared in a chi-square test (2 × 2). This value gives you an indication of the extent of the relationship between the two variables. Cramer's phi can be used for even larger comparisons. It is a more meaningful measure of the practical significance of the chi-square test and is reported as the effect size.

See also

★ General likelihood-ratio tests, which are approximately chi-square tests

★ McNemar's test, related to a chi-square test

★ The Wald test, which can be evaluated against a chi-square distribution

External links

★ Chi-Square Calculator from GraphPad

References

1. Aaron, B., Kromrey, J. D., & Ferron, J. M. (1998, November). Equating r-based and d-based effect-size indices: Problems with a commonly recommended formula. Paper presented at the annual meeting of the Florida Educational Research Association, Orlando, FL. (ERIC Document Reproduction Service No. ED433353)